This paper proposes a critical synthesis about different theories of time in physics and a new interpretation of its operational reality. We built it on two, deeply analyzed, fundamental ideas: the mathematical nature of Newtonian and relativistic time and the consequent need to build physical theories of time starting from the measurements obtained by real clocks. We observe that relativistic theories refer to axiomatic assumptions about clocks, probably not verified by experiments if we use clocks of different construction. We propose (...) the concept of evolutionary internal time and we conclude that a new interpretation of the nature of physical time should arise from a deep and accurate reflection about the rate of clocks. We believe that this approach to the question could open new theoretical perspectives about the evolution of physical systems. (shrink)